French Pat. No. 1.500.741 presents a resiliently bendable loop fastening device which functions to fasten the hook of a garment hanger directly to a clothesline and which operates in an entirely different manner from that of the devices set forth herein. Danish Patent No. 73678 presents a spring clip device which is installed on the inside area of a garment hanger hook to fasten the hook to a linear member. Norwegian Patent No. 118789 shows devices resembling peg-type clothespins which are used to frictionally restrain a garment hanger hook in its position on a clothesline or, alternatively, to suspend the hook below the clothesline. U.S. Pat. No. 1,273,809 shows a wire clamp having some similarities to certain embodiments of the clasping devices set forth herein. U.S. Pat. No. 2,474,429 combines a generally L-shaped bracket with a closely matched garment hanger hook to provide means for closing the opening of the hook, but which is not realistically capable of forcefully clamping the hook to a supporting linear member. U.S. Pat. No. 3,202,329 shows a highly modified garment hanger hook having an elongated slot at its upper section to receive a clothesline and a specially modified clothespin to clamp across and to close the opening of the slot in order to retain the clothesline in the slot. U.S. Pat. Nos. 1,690,614 and 3,048,311 present highly modified garment hanger hooks which include means for locking the hook to a supporting clothesline. U.S. Pat. No. 3,240,462 presents a clamping device which replaces the hook of a garment hanger and which provides means for positively clamping the garment hanger to a clothesline. U.S. Pat. Nos. 2,915,274 and 3,184,204 show devices which can be suspended from a clothesline and which, in turn, have means for suspending a garment hanger hook from the device itself. U.S. Pat. Nos. 135,882; 485,758; 733,921; and 2,542,224 show devices which bear some resemblance to certain embodiments of the clasp presented herein.